Question

Consider the triangle shown below where m∠C=51∘, b=10 cm, and a=21 cm.Use the Law of Cosines to determine the value of x (the length of AB in cm).x=

Answer 1

The law of cosines states that we can find the measure of a non-right triangle if we know the measurement of the opposite angle and the two other sides, it can be written like this.

$c^2=a^2+b^2-2\cdot a\cdot b\cdot\cos (C)$

since we know the measurement of C (51°) and the length of a and b (21cm and 10cm), apply the law of cosines to find the value of c

$\begin{gathered} c^2=(21)^2+(10)^2-(21\cdot10\cdot\cos (51)) \\ c^2=441+100-210\cos 51 \\ c^2\cong208.842 \\ c\cong\sqrt[]{208.842} \\ c\cong14.45 \end{gathered}$